Heavy traffic limits for join-the-shortest-estimated-queue policy using delayed information

Rami Atar, David Lipshutz

Research output: Contribution to journalArticlepeer-review


We consider a load-balancing problem for a network of parallel queues in which information on the state of the queues is subject to a delay. In this setting, adopting a routing policy that performs well when applied to the current state of the queues can perform quite poorly when applied to the delayed state of the queues. Viewing this as a problem of control under partial observations, we propose using an estimate of the current queue lengths as the input to the join-the-shortest-queue policy. For a general class of estimation schemes, under heavy traffic conditions, we prove convergence of the diffusion-scaled process to a solution of a so-called diffusion model, in which an important step toward this goal establishes that the estimated queue lengths undergo state-space collapse. In some cases, our diffusion model is given by a novel stochastic delay equation with reflection, in which the Skorokhod boundary term appears with delay. We illustrate our results with examples of natural estimation schemes, discuss their implementability, and compare their relative performance using simulations.

Original languageEnglish
Pages (from-to)268-300
Number of pages33
JournalMathematics of Operations Research
Issue number1
StatePublished - 1 Feb 2021


  • Delays
  • Heavy traffic limits
  • Join the shortest estimated queue
  • Load balancing
  • Oscillations
  • State-space collapse

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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